One would think David Stockman wouldn't have the warmest memories about the Hay-Adams Hotel. It was there that he met for several breakfasts with writer William Greider, resulting in the December 1981 Atlantic magazine article titled "The Education of David Stockman." The article was an embarrassment to the administration, and the budget director's stock with the president slipped considerably. Now all seems well again for him and he has chosen the Hay-Adams as the site of his marriage to Jennifer Blei tomorrow. Blei made ceremony and reception arrangements yesterday with Danielle Mosse, for whom the hotel's dining room Le Danielle is named and whose husband, George, owns the Hay-Adams.

A United States senator does not become a United States senator without understanding one of the truly important issues, such as parking. Sen. Robert Dole recently asked the Senate Rules Committee not to build a fast-food shop in the basement parking garage between the Dirksen and Hart buildings. Some 25 parking places would be eliminated by the restaurant, including one belonging to the Kansas Republican, conveniently located a few steps from an elevator that takes him to his office. Dole's letter to Rules Chairman Charles McC. Mathias (R-Md.), and one to each of his 99 Senate colleagues seeking their support in the fight, has stopped initial work on the restaurant. Dole said he was concerned about the closing of the C Street entrance to the Hart building for "safety considerations." A Dole staff aide said that during the senator's 1976 presidential campaign, there had been a bomb scare involving his car.

Helene Von Damm, the former White House personnel chief, couldn't have chosen a better time to visit Vienna. President Reagan's nominee to become the new U. S. ambassador to Austria arrived just in time for the Vienna carnival season, and she and her husband, Byron Leeds, planned to attend last night's Opera Ball, the highlight of the festivities. The couple is traveling with William Clark, the national security adviser. Von Damm was born in Austria and spent her early childhood there. Her nomination has not yet been sent to the Senate for confirmation and it will be several weeks before she can take up her duties as the first U. S. ambassador to Austria in two years. She told reporters that she often dreamed of attending the annual gala and would not comment on her pending diplomatic duties. "I hope I'm a good dancer," she said.

The 17-year-old Massachusetts high school senior made enough noise about not being able to have her ambition published in her school yearbook. She wanted to become a Playboy Magazine centerfold, and Playboy noticed. Dan Sheridan, a spokesman for the magazine, said he would personally see to it that the photo editors at Playboy would look at Loretta Martin's picture. Sheridan warned that the magazine gets hundreds of pictures every day and there are only 12 centerfolds a year. Martin, who has contacted an American Civil Liberties Union lawyer to help get her ambition published in the Billerica High School yearbook, said, "Of course, I can't pose nude until I'm 18, and I have to lose 20 pounds before I pose at all."

The Kennedy Center production of "Toyer" closes tomorrow night after only two weeks of a six-week run. Finding a quick substitute for the panned "Toyer," Kennedy Center chairman Roger L. Stevens will put in its place a production of "You Can't Take It With You," a 1937 Pulitzer Prize winner by Moss Hart and George S. Kaufman. Opening on Feb. 22 for a five-week engagement, the play will star Tony Award winners Jason Robards, Colleen Dewhurst, George Rose and Elizabeth Wilson.

Navy cooks have one small concern when Queen Elizabeth tours the aircraft carrier USS Ranger in San Diego harbor later this month. They have prepared a royal meal including a clam or fish chowder, California langosta, creamed peas and mushrooms, baked potatoes with sour cream, a salad, rolls and cherry or apple pie, but Washington brass will have to decide if a California dry wine can be served. Alcoholic beverages are not permitted on U.S. Navy ships, but are allowed during visits by foreign dignitaries. That approval, however, must come from the secretary of the Navy.

"Modern first ladies show their support for good causes like this one a little differently than our first first ladies," Nancy Reagan explained. "Dolley Madison supported the Washington Orphan's Asylum by giving $5 and a cow. Well, you'll be relieved to hear that I have not brought a cow." Mrs. Reagan told the Women's Board of the American Heart Association, Nation's Capital affiliate, luncheon yesterday in the Washington Hilton that she was donating $3,000, the fee she received for an article she wrote about her father, Dr. Loyal Davis, who died last August of heart failure. The article will appear in the Father's Day issue of McCall's Magazine. Among the wives of top administration officials attending were Ann Regan, Jean French Smith, Suzanne Block, Jane Weinberger and Sophia Casey.

Oil tycoon J. Paul Getty Jr., one of the richest men in the world, is "on the brink of a settlement" with his penniless son, J. Paul Getty III, who sued him for $25,000-a-month medical support after suffering a debilitating stroke in 1981, a family spokesman says. "The father is facing the legal realities," said the younger Getty's godfather, William A. Newsom, a state appellate judge in San Francisco. "His case was a poor one, and that's putting it charitably, given his monstrous income." The elder Getty is the reclusive son of the late oil billionaire J. Paul Getty, who once refused to pay ransom to the younger Getty's kidnappers, but relented after they cut off one of his ears and sent it to his mother.